UNLV Theses, Dissertations, Professional Papers, and Capstones
2009
Two-tank indirect thermal storage designs for solar
parabolic trough power plants
Joseph E. Kopp
University of Nevada Las Vegas
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TWO-TANK INDIRECT THERMAL STORAGE DESIGNS FOR SOLAR
PARABOLIC TROUGH POWER PLANTS
By
Joseph E. Kopp
Bachelor of Arts in Physics
Lewis & Clark College
2004
A thesis submitted in partial fulfillment
of the requirements for the
Master of Science Degree in Mechanical Engineering
Howard R. Hughes College of Engineering
Department of Mechanical Engineering
Graduate College
University of Nevada, Las Vegas
August 2009
ABSTRACT
Two-Tank Indirect Thermal Storage Designs for
Solar Parabolic Trough Power Plants
by
Joseph Kopp
Dr. Robert F. Boehm, Examination Committee Chair
Professor of Mechanical Engineering
University of Nevada, Las Vegas
The performance of a solar thermal parabolic trough plant with thermal
storage is dependent upon the arrangement of the heat exchangers that
ultimately transfer energy from the sun into steam. The steam is utilized in a
traditional Rankine cycle power plant. The most commercially accepted thermal
storage design is an indirect two-tank molten salt storage system where molten
salt interacts with the solar field heat transfer fluid (HTF) through a heat
exchanger. The molten salt remains in a closed loop with the HTF and the HTF
is the heat source for steam generation. An alternate indirect two tank molten
salt storage system was proposed where the molten salt was utilized as the heat
source for steam generation. A quasi-steady state simulation code was written to
analyze the key environmental inputs and operational parameters: solar
radiation, solar field size, thermal storage system, heat exchangers, and power
block. A base case with no thermal storage was modeled using design
parameters from the SEGS VI plant and the effects of solar field size were
analyzed. The two differing indirect two-tank molten salt storage designs were
modeled and their solar field size and thermal storage capacity were treated as
parameters. Results present three days of distinct weather conditions for Las
iii
Vegas, Nevada. Annual and monthly electricity generation was analyzed and the
results favor the thermal storage case with the solar field HTF interacting with
steam. Additionally, the economic trade offs for the three arrangements and
speculation of operating strategies that may favor the alternate storage design is
discussed.
iv
TABLE OF CONTENTS
ABSTRACT .......................................................................................................... iii
LIST OF FIGURES .............................................................................................. vi
LIST OF TABLES ................................................................................................vii
NOMENCLATURE ............................................................................................. viii
ACKNOWLEGEMENTS ...................................................................................... ix
CHAPTER 1 INTRODUCTION ......................................................................... 1
Background ..................................................................................................... 1
Review of Plant Modeling ................................................................................ 4
Solar Parabolic Trough Plant ........................................................................... 6
Storage Oil-Water Design .............................................................................. 10
Storage Salt-Water Design ............................................................................ 13
CHAPTER 2 HEAT TRANSFER RELATIONS ............................................... 16
Solar Field Heat Transfer Fluid ...................................................................... 16
Nitrate Salt ..................................................................................................... 17
Overall Heat Transfer Coefficient .................................................................. 19
CHAPTER 3 MODEL COMPONENTS ........................................................... 24
Weather Reader and Solar Field ................................................................... 24
Heat Exchangers ........................................................................................... 26
Oil-Water .................................................................................................. 28
Oil-Salt and Salt-Oil .................................................................................. 30
Salt-Water................................................................................................. 31
Turbine .......................................................................................................... 33
Mixer and Power Plant Simplification ............................................................ 36
Storage Tanks and Storage Controls Logic ................................................... 37
CHAPTER 4 RESULTS .................................................................................. 43
No Storage .................................................................................................... 43
Storage Oil-Water .......................................................................................... 52
Comparisons of Storage Designs .................................................................. 61
CHAPTER 5
CONCLUSIONS AND RECOMMENDATIONS ......................... 69
APPENDIX A MATLAB CODE ......................................................................... 72
REFERENCES ................................................................................................... 87
VITA ................................................................................................................... 85
v
LIST OF FIGURES
Figure 1: SEGS III to SEGS VII in Kramer Junction, California [1] ..................... 1
Figure 2: Nevada Solar One [2] .......................................................................... 2
Figure 3: Thermal storage tanks at Andasol 1 [4] ............................................... 3
Figure 4: General solar parabolic trough plant design [11] ................................. 7
Figure 5: Abbreviated Ts Diagram for design points of SEGS VI Power Cycle .. 9
Figure 6: Plant design with thermal storage [11]............................................... 11
Figure 7: Storage Salt-Water design for indirect two tank thermal storage [11] 14
Figure 8: Specific heat of nitrate salt and Therminol VP-1™ ............................ 19
Figure 9: Heat transfer dependency on temperature per kg of fluid.................. 22
Figure 10: Heat transfer coefficients as products of variable components ......... 23
Figure 11: Flow chart for power plant components ............................................. 24
Figure 12: Temperature assignments for the steam train ................................... 28
Figure 13: Representation of Nexant [17] molten salt steam train ...................... 33
Figure 14: Temperature loss in 6 Hour Cold Tank, half full ................................ 40
Figure 15: Storage Controls for Storage Oil-Water case .................................... 41
Figure 16: Storage controls for Salt-Water Storage ............................................ 42
Figure 17: Hourly power totals for July 7, a typical sunny day ............................ 44
Figure 18: Hourly power totals for August 6, a day with afternoon clouds .......... 45
Figure 19: Hourly power totals for December 1st, a clear winter day. ................ 46
Figure 20: Gross power generation for July 7 with several solar field sizes ....... 47
Figure 21: Gross power generation for August 6 with several solar field sizes ... 48
Figure 22: Gross power generation for Dec 1 with several solar field sizes ....... 49
Figure 23: Power versus water mass flow rate for the No Storage case ............ 50
Figure 24: July 7th with four hours of thermal storage, varying solar multiple ..... 52
Figure 25: Aug 6th with four hours of storage, varying solar multiple .................. 53
Figure 26: Dec 1st with four hours of storage, varying solar multiple .................. 54
Figure 27: July 6th with ten hours of storage, varying solar multiple ................... 56
Figure 28: Aug 6th with ten hours of storage, varying solar multiple ................... 57
Figure 29: Monthly gross energy output for the No Storage Case ...................... 58
Figure 30: Monthly gross energy output for Storage Oil-Water with 8 hour tank. 59
Figure 31: Monthly gross energy output for solar multiple of 1.4 ........................ 60
Figure 32: Storage designs for July 7, SM 1.6 and 4 hours of storage ............... 61
Figure 33: Storage designs for July 7, SM 2 and 10 hours of storage ................ 63
Figure 34: Storage designs for August 6, SM 1.6 and 4 hours of storage .......... 64
Figure 35: Storage designs for Dec 1, SM 1.6 and 4 hours of storage ............... 65
vi
LIST OF TABLES
Table 1: UA values for steam train ..................................................................... 29
Table 2: Heat transfer design conditions for steam train heat exchangers ......... 29
Table 3: Reference conditions for reheater temperatures .................................. 30
Table 4: Design conditions for oil-salt heat exchangers ..................................... 31
Table 5: Design conditions for molten salt steam train ....................................... 32
Table 6: Correlation of turbine inlet pressure and water mass flow rate ............. 35
Table 7: Physical properties of thermal storage tanks ........................................ 38
Table 8: Annual energy totals for No Storage ..................................................... 66
Table 9: Normalized annual energy generation .................................................. 68
vii
NOMENCLATURE
Ai , Ao
cp , cp1 , cp2
D , Do , Di
dT
DNI
ε , ε decrease , ε ref
= Heat exchanger surface area [m²]
= Specific heat capacity [J/kgK]
= Diameter of tube inside shell and tube heat exchanger [m]
= Incremental change in temperature [°C]
= Direct normal irradiance [W/m²]
= Isentropic efficiency
EndLoss
= Amount of sunlight reflected off the end of an SCA unit
= Thermal efficiency of the solar field
η field
η HCE
h , hi , ho
hin , hout , hmix
IAM
k
L
M tan k
m&
μ
Nu
P
Pr
Q& abs
Q&
collected
= Thermal efficiency of the heat collection element
= Fluid heat transfer coefficient [W/m²K]
= Fluid enthalpy [J/kg]
= Incidence angle modifier
= Thermal conductivity [W/m²K]
= Length of heat exchanger tubes [m]
= Mass [kg]
= Mass flow rate [kg/s]
= Dynamic viscosity [Pa s]
= Nusselt Number
= Pressure [bar]
= Prandtl number
= Energy rate absorbed by solar field [W]
= Heat rate collected by solar field [W]
Q& pipe _ loss
Q&
= Heat loss rate in pipes through solar field to power block [W]
Q
R" fi , R" fo
= Energy [J]
= Fouling resistance inside heat exchanger [m2K/W]
Re D
RowShadow
SFAvail
T , Ttan k
= Reynolds number
= Fraction of solar radiation not blocked by neighboring SCA units
= Fraction of year the solar field is in operation
= Temperature [°C]
= the elevation angle between the sun and zenith
= Heat exchanger overall heat transfer coefficient [W/K]
receiver _ loss
θ
UA
= Heat loss rate in heat collection element [W]
Subscript Terms
i, o
= ‘i’ indicates within tube, ‘o’ indicates outside of tube
= Value at reference/design conditions
ref
viii
ACKNOWLEDGEMENTS
I would like to thank Dr. Robert Boehm for the opportunity to work at the
Center for Energy Research and for providing me with many tools for
professional growth. I would also like to thank every one at the Solar Site, past
and present, who have helped me along the way. Finally, I would like to thank
my parents and siblings who are always there providing me with non-technical
support.
ix
CHAPTER 1
INTRODUCTION
Background
Concentrating solar thermal power for utility-scale electricity generation is
experiencing unprecedented growth. The three major divisions within
concentrating solar thermal power are parabolic troughs, solar towers, and dish
Stirling technology. Parabolic trough power plants are considered to be the most
commercially ready technology.
Groundwork for commercial parabolic trough power plants was developed by
the Luz International Limited from 1984 to 1990. A total of nine solar plants,
ranging from 30-80 megawatts electric (MWe) were constructed in California and
continue to operate today. The sixth solar electric generating systems (SEGS)
plant, SEGS VI, included in Figure 1, has become the focal point of published
research on parabolic trough power plants. The design conditions for this study
were based on information provided for the 35 MWe SEGS VI plant.
Figure 1: SEGS III to SEGS VII in Kramer Junction, California [1]
1
In 2007, Nevada Solar One, a 64 MWe parabolic trough power plant, began
operations near Las Vegas, Nevada. Acciona Solar Power operates the plant,
shown in Figure 2, and it was the first utility-scale parabolic trough power plant
built in the new millennium. This plant has been operating well for the past two
years.
Figure 2: Nevada Solar One [2]
Construction finished on Andasol 1, shown in Figure 3, in November 2008.
This plant is designed with a molten salt storage system capable of 7 hours of
full-capacity power production. This is the first commercial parabolic trough plant
to implement a molten salt two tank storage system. Thermal storage was
utilized in SEGS I but the storage medium was the synthetic oil solar field heat
2
transfer fluid, or HTF. Synthetic oils are no longer considered for a storage
medium in part due to their higher cost [3].
Figure 3: Thermal storage tanks at Andasol 1 [4]
The future of parabolic trough technology is bright as there are over 1000 MW
of plants under construction and even more have been announced [5]. Many of
these plants claim thermal storage will be integrated into their plant design.
The principle advantages of thermal energy storage in a solar parabolic
trough power plant are the ability to control the time and quantity of power
production. Herrmann [6] asserts thermal storage can be applied for: buffering
3
during transient weather conditions, dispatchability, increased annual capacity
factor, and more even distribution of electricity production. Thermal storage can
provide the stability necessary for base load operation and it also can have the
economic advantage to discharge surplus power during peak demand hours.
Additionally, the annual solar-to-electric efficiency can improve as a result of
thermal storage. Price [7] showed that the improvements to turbine start-up,
excess heat from the field, improved parasitic losses, and negligible energy loss
from “below turbine minimum” outweigh the storage thermal losses and reduced
power plant steam cycle efficiency due to storage.
Review of Plant Modeling
In 1995, Frank Lippke [8] published results from a model of the SEGS VI plant
that used EASY simulation software. His work included reference design values
for the power block and several equations he presented were utilized in the
current study. One objective of his work was to examine how to optimize the
HTF’s solar field outlet temperature and flow rate. His results suggest the
highest allowed HTF temperature is optimum for a summer day; however during
fall and winter conditions the superheating temperature should not greatly
exceed the design value.
The Solar Advisor Model, SAM [9], is modeling software developed by the
National Renewable Energy Laboratory. The publicly available source code is
written in FORTRAN, is, and runs off software called TRNSYS. SAM is a work in
progress and its current state does not represent a complete thermophysical
4
model of a solar parabolic trough power plant. As a result, it could not be used to
perform the desired parametric studies. Among the benefits of this program,
however, are rapid computations and calculations of levelized cost of energy.
TRNSYS has a large set of solar parabolic trough power plant components.
The solar thermal electric component library, STEC, is organized by the
international organization SolarPACES. A model of SEGS VI was available that
utilized STEC components; however the complex model had convergence
issues.
Numerous private parabolic trough power plant models exist, such as
PCTrough™ by Solar Millennium, but they are not accessible in the public
domain. Patnode [10] performed a detailed simulation of SEGS VI using
Engineering Equation Solver, EES, and TRNSYS. Equations and design values
presented by Patnode were also used utilized in this work.
A new solar parabolic trough power plant model was built for this study using
Matlab™. The code reflects the design considerations of the 35 MWe SEGS VI
plant, though modeling the precise performance of the plant was out of the scope
of this project. Absolute precision was not necessary when the objective was to
consider the behavioral differences of competing storage designs applied to the
same solar field and weather conditions. The code was written to calculate the
gross electrical power but not parasitic losses. For each power plant design the
solar field size and the storage tank sizes were treated as parameters.
Data from the Typical Meteorological Year 3, TMY3, was utilized for local
weather conditions. Component calculations were performed for a one second
5
interval to maintain scientific units. Values for power were calculated hourly.
This model will allow smaller time increments than hourly values given by TMY3.
Hourly energy totals were found with ease since the MW produced in one second
integrated over an hour equal the accepted energy unit of mega-watt hours
(MWh).
Solar Parabolic Trough Plant
The cornerstone of solar parabolic trough plant is the solar field. The solar
field consists of parabolic trough collectors and piping. Parabolic trough
collectors can be divided into two subsystems: the solar collection assembly
(SCA) and the heat collection element (HCE).
A highly reflective material covers the parabolic surface area of the SCA. The
SCA also includes the single-axis tracking equipment and support structure for
the HCEs. Typically the SCA units are aligned along the North-South axis and
track the sun from East to West. During operation, solar radiation is reflected
from the SCA onto the parabolic trough’s focal line, where the HCE resides.
The outer glass shell of the HCE receives approximately 75 times the
amount of direct normal irradiation (DNI) as a non-concentrated surface. When
radiation is transmitted through the glass shell it passes through a vacuum and
arrives at the absorber tube. Vacuum conditions prevent conduction and
convection heat losses from the absorber tube to the environment. The absorber
tube’s outer surface is covered in a ceramic metal (cermet) coating designed to
minimize radiation losses in the infrared region of the electromagnetic spectrum.
6
The absorber tube conducts thermal energy to its inner surface and provides the
heat source for the HTF flowing within the tube. The HTF receives heat from the
inner surface through convection, conduction, and radiation.
The solar field depicted in Figure 4 heats the HTF (red line) that travels
through piping to the power block. The flow is separated in the power block into
two parallel heat exchanger elements: the steam train and the reheater.
Figure 4: General solar parabolic trough plant design [11]
7
The steam train is a term used to describe the heat exchangers that heat the
working fluid, highly pressurized water, from a compressed liquid state into a
superheated vapor state. The preheater warms the working fluid from
compressed liquid to saturated liquid. Water boils in the steam generator and
exits as a saturated vapor. Due to the latent heat of evaporation the steam
generator is the most energy intensive heat exchanger. The superheater utilizes
the highest temperature HTF to heat the saturated vapor into superheated
steam.
The superheated steam performs work on a high pressure turbine and
typically loses enough heat to enter the saturation region. An abbreviated
temperature-entropy (Ts) diagram for power cycle design conditions for SEGS VI
[8] is shown in Figure 5. The design conditions illustrate the ideal case where the
working fluid reaches the saturated vapor state. The reheater serves to
superheat the steam a second time. The pressure of the steam exiting the
reheater has been reduced and is utilized to perform work on a low pressure
turbine. There are two high pressure turbine stages and five low pressure
turbine stages for a total of seven turbine stages.
The quantity and size of each type of heat exchanger will vary given the size
of a plant. Heat exchangers can only reach a functional length before the
surface area demands require additional units. For modeling purposes a control
volume approach eliminates the need for actual heat exchanger dimensions.
8
Ts Diagram of Power Cycle
500
450
400
Temperature [C]
350
300
250
200
150
100
50
0
0
1
2
3
4
5
6
7
8
9
10
Entropy [kJ/kgK]
Figure 5: Abbreviated Ts Diagram for design points of SEGS VI Power Cycle
Steam exiting the low pressure turbine undergoes a phase change in the
cooling process so water can be pumped to the preheater and the cycle can
repeat. Cycle completion for the HTF includes passing through the expansion
vessel, which among several functions, serves as a mixing unit.
The mass flow rate and HTF outlet temperature from the solar field are
important values. Generally, a higher mass flow rate from the field will translate
into a higher mass flow rate of steam but at the cost of lower temperature. The
highest field outlet temperature can provide the highest steam enthalpy into the
turbine but at a cost of lower water flow rate. It has been suggested by another
9
author that neither strategy displays a significant improvement in overall plant
performance [10]. Some models treat both values as outputs while this model
treats the HTF outlet temperature as a parameter. The operating strategy in this
model was chosen to maximize outlet temperature since the highest quality of
thermal storage is desirable.
The solar multiple is defined as the solar collector area divided by the solar
collector area necessary for nominal power generation. The solar collector area
necessary to generate nominal power is considered to be a fundamental design
condition for a plant. The design condition may be chosen for a direct normal
irradiation level (DNI) of 800 W/m2 or the typical solar radiation value at noon on
the spring equinox [3]. The design of SEGS VI was assumed have a solar
multiple (SM) equal to one. A plant optimized at SM 1 has the potential to collect
a surplus of solar energy under high solar radiation periods. The amount of
surplus energy, however, does not justify the costs of implementing thermal
storage. An increase in SM will increase the collector area in the solar field and
will lead to more thermal energy available for storage. If solar energy cannot be
collected or stored, parasitic losses are reduced by moving SCA units to stow
and maintaining design flow rate conditions.
Storage Design Oil-Water: Synthetic Oil Steam Generation
Indirect two-tank thermal storage can be integrated into a parabolic trough
plant, as shown in Figure 6. This is the most commercially ready thermal storage
design and may be referred to as Storage Oil-Water because the synthetic oil
10
HTF is the heat source in steam generation. While actual operational schemes
may be quite complex, the addition of thermal storage does not have to
significantly affect the overall operating strategy.
Figure 6: Plant design with thermal storage [11]
The basic operating strategy is to charge thermal storage when the HTF flow
rate exceeds the design flow rate for steam generation. Surplus flow travels
through the oil-to-salt shell and tube heat exchanger to charge molten salt then
11
exits to the expansion vessel. During charging, molten salt leaves the cold tank
extracts heat from the HTF, and then enters the hot tank.
Ideally the design flow rate of HTF is maintained during operating hours so
discharging from the hot tank should be performed to maintain the maximum
HTF flow rate through the steam train and reheater. Discharging salt from the
hot tank to reheat the HTF occurs in the same heat exchanger except flow is
reversed. Salt is always maintained on the shell side of the heat exchangers
[12].
The first law of thermodynamics requires a temperature drop across a heat
exchanger. The temperature of the HTF heated by discharging salt will be lower
than the HTF temperature directly from the solar field because the heat has
passed through two heat exchangers and an associated heat loss inside the hot
tank. This decrease in temperature will result in a decrease in power generation.
The required volume of molten salt is considered to be the volume required
to completely fill one tank. Consequently, if one tank is completely filled the other
tank is empty. This is a simplification of the actual system, where a minimum
volume of salt must be maintained within each tank [13]. When fully charged all
the molten salt resides in the hot salt tank at maximum temperature of 386 °C.
The design temperature of the cold salt tank is 293°C. The tanks are considered
to be fully mixed thermally and have a heat loss correlation based on surface
area of tank.
The oil-to-salt heat exchanger must be sized for the discharging capacity of
the HTF at the design flow rate for steam generation. Therefore the size of the
12
heat exchangers must be optimized to transfer heat to the design HTF flow rate.
If a solar field was designed for 800 W/m2, then a solar multiple of 1.6 with DNI of
1,000 W/m2 would provide double the HTF design flow rate. For any larger solar
multiple, the oil-to-salt heat exchanger area must increase and subsequently its
cost will increase.
To charge the HTF, the necessary flow rate is withdrawn from the expansion
vessel and is mixed with HTF flow from the solar field, if there is any. If there is
not enough heat in storage to bring the mass flow rate up to design flow, but
enough hot molten salt to generate the minimum amount of power, the hot
molten salt is discharged completely. Four MWe was the minimum amount of
power assumed necessary for electricity generation. This corresponded to an oil
mass flow rate of 40 kg/s. If the HTF flow rate could not reach 40 kg/s, even
after thermal storage discharge, the hot salt would dwell in the hot tank and
power would not be generated.
Storage Salt-Water: Molten Salt Steam Generation
The indirect two-tank molten salt storage proposed in Figure 7 is referred to
as Storage Salt-Water. This is because molten salt is the heat transfer fluid in
the steam train and reheater. The synthetic oil is contained in a closed loop
around the solar field and the oil-salt heat exchangers. Although not illustrated,
an expansion vessel will still be needed for the solar field.
13
Figure 7: Storage Salt-Water design for indirect two tank thermal storage [11]
A significant difference between thermal storage plant designs is the number
of heat exchangers encountered before transferring heat to the working fluid. No
additional heat exchangers are required between the HTF and the working fluid
during normal operating conditions for Storage Oil-Water. However, when heat
is needed from storage, two additional heat exchangers are utilized. Heat is first
transferred from oil to salt, then from salt back to oil, and finally from oil to the
14
working fluid. The Storage Salt-Water design utilizes two heat exchangers
between the synthetic oil and the working fluid for all operations.
Storage Salt-Water requires a larger oil-salt heat exchanger area than the
Storage Oil-Water case because all of the solar field HTF flow rate must transfer
heat to the salt. While the heat exchanger area for Storage Oil-Water does not
have to increase until SM 1.6, any increase in solar multiple for Storage SaltWater will result in a larger oil-salt heat exchanger area. Based on the cost of oilsalt heat exchangers, Storage Oil-Water is heavily favored.
Integration of thermal energy storage decreases a plant’s efficiency for the
time period of thermal discharging. This is due to inevitable heat transfer losses
to charge the thermal storage medium and also to discharge it. Molten salt is a
leading medium for thermal storage and there is discussion it may be circulated
through the solar field [14], thus reducing thermal losses through heat exchange.
The description of the molten salt steam generation is also crucial to the
analysis of the Storage Salt-Water design. The behavior of molten salt as a heat
transfer fluid is discussed in Chapter 2 and its design values compared to oilwater heat exchanger design values are presented in Chapter 3.
15
CHAPTER 2
HEAT TRANSFER RELATIONS
Solar Field Heat Transfer Fluid
The synthetic oil used as the solar field heat transfer fluid is a eutectic mixture
of diphenyl oxide and biphenyl. Two commercial names for this product are
Therminol VP-1™ and Dithers A™. It is stable up to 399 °C. The thermal
properties of this mixture were selected from the SAM [9] source code and
equations 1-4 describe them as functions of temperature. Included also as
equation 5 is a relationship for temperature as a function of enthalpy.
Therminol VP-1™:
cp(T ) = 1000 ⋅ (1.509 + 0.002496 ⋅ T + 0.0000007888 ⋅ T 2 )
[J/kg/K]
k (T ) = 0.1381 − 0.00008708 ⋅ T − 0.0000001729 ⋅ T 2
[W/m/K]
μ (T ) = 0.001 ⋅ (100.8703 ⋅ T ( 0.2877 + Log (T
[Pa s]
−0.3638
))
)
(1)
(2)
(3)
h(T ) = 1000 ⋅ (−18.34 + 1.498 ⋅ T + 0.001377 ⋅ T 2 )
[J/kg]
(4)
T (h) = −0.000000000158 ⋅ h 2 + 0.0006072 ⋅ h + 13.37
[°C]
(5)
16
Nitrate Salt
The molten salt chosen was a nitrate salt that is composed of 60% KNO3 and
40% NaNO3. Thermal properties for solar salt were found in SAM [9] and listed
in equations 6-9. Among the benefits of the nitrate salt is its stability up around
600 °C. However, a disadvantage is its high melting point; Schulte-Fischedick
[13] report that local solidification can occur at 239 °C.
Nitrate Salt:
cp(T ) = 1443 + 0.172 ⋅ T
[J/kg/K]
(6)
k (T ) = 0.443 + 0.00019 ⋅ T
[W/m/K]
(7)
μ (T ) = 0.001 ⋅ (22.714 − 0.12 ⋅ T + 0.0002281 ⋅ T 2 − 0.0000001474 ⋅ T 3 )
(8)
[Pa s]
T (h) = 0.001 ⋅ (22.714 − 0.12 ⋅ T + 0.0002881 ⋅ T 2 − 0.0000001474 ⋅ T 3 )
[°C]
(9)
The temperature of the cold tank is of concern because long periods without
charging may lead to freezing conditions. Freezing is a distinct possibility if the
salt is not heated by auxiliary heaters and a study showed the cold tank dropped
from 293 °C to 239 °C in 50 days (without auxiliary heating) [13]. For a plant with
a solar multiple close to one, there will be concerns of salt solidification in the
winter months, when the flow rate of the field does not exceed design conditions.
Freezing would not occur in the normal operations of the Storage Salt-Water
case.
17
Despite freezing concerns, nitrate salt has been proven reliable and Relloso
[4] states it was chosen as the storage media for Andasol 1. Auxiliary heaters
were not included in this analysis, and the salt was allowed to drop below the
freezing point (phase change was neglected). During charging the HTF had to
supply additional heat to overcome the lower temperatures. This thermal energy
requirement can be related to an internal parasitic loss.
Nitrate salt has a lower heat capacity than Therminol VP-1™ as shown in
Figure 8. This is particularly important in the development of the molten salt
steam train because it determines how much heat can be provided to each heat
exchanger stage. In particular, the steam generator requires a larger
temperature difference of molten salt. It is also important in the development of
the oil-salt heat exchangers, as the salt flow rate must be higher than the oil flow
rate to match the heat exchanged. Higher mass flow rate also represents higher
pumping power losses. Pumping power losses are further augmented by nitrate
salt’s higher viscosity.
18
Specific Heat Capacity vs Temperature
2.8
Enthalpy
[J/kg]
Specific
Heat [kJ/kgK]
2.6
2.4
2.2
2
1.8
1.6
1.4
Nitrate Salt
1.2
1
200
Therminol VP-1
250
300
350
400
Temperature [C]
Figure 8: Specific heat of nitrate salt and Therminol VP-1™
Overall Heat Transfer Coefficient
The thermal properties of the two heat transfer fluids are further analyzed by
their capabilities of transferring heat. The overall heat transfer coefficient
applicable to shell and tube heat exchangers is determined by
R" fi ln Do / Di R" fo
1
1
1
,
=
+
+
+
+
UA hi Ai
Ai
2πkL
Ao
ho Ao
(10)
from Incropera and Dewitt [15]. UA can be found for design conditions, however
with an energy source as variable as the sun, off-design conditions occur often.
19
According to solar literature, the approximation for modeling the UA during offdesign conditions is
⎛ m&
UA
=⎜
UAref ⎜⎝ m& ref
⎞
⎟
⎟
⎠
0.8
,
(11)
where the mass flow rate has been determined to be the dominant variable in
UA. Patnode [10] provides a thorough derivation of this term and certain aspects
are highlighted here. By neglecting the thermal resistance through the metal
tubes and the resistance due to fouling is negligible, equation (10) becomes
1
1
1
.
=
+
UA hi Ai ho Ao
(12)
Equation (12) implies that the behavior of UA is dominated by convective heat
transfer. The contact surface area for each fluid and the heat transfer coefficient
of the fluids on the inside and the outside of the tubes are the only values
considered. Surface area will not change during off-design conditions so further
a relative UA approximation can be performed by
1
1 1
∝ + .
UA hi ho
(13)
The heat transfer coefficient is defined as
h=
Nu ⋅ k
D
(14)
where the Nusselt number for fully developed (hydrodynamically and thermally)
turbulent flow in smooth circular tubes is
20
Nu D = 0.023 ⋅ Re 0D.8 ⋅ Pr n .
(15)
For a cooling fluid where n = 0.3 and for a heating fluid n = 0.4. The Reynolds
number is solved by
Re D =
4 ⋅ m&
,
π ⋅D⋅μ
(16)
and the Prandtl number in equation (15) is
Pr =
μ ⋅ cp
k
.
(17)
Solving the Nusselt number for the heating fluid (n=3) gives
0.8
Nu D = 0.023 ⋅ Re ⋅ Pr
0.8
D
0.3
⎛ 4 ⋅ m& ⎞ ⎛ μ ⋅ cp ⎞
⎟⎟ ⋅ ⎜
= 0.023 ⋅ ⎜⎜
⎟ .
⎝π ⋅ D⋅μ ⎠ ⎝ k ⎠
0.3
(18)
After incorporation of all the terms the heat transfer coefficient becomes
0.8
⎛ 4 ⋅ m& ⎞ ⎛ μ ⋅ cp ⎞
⎟ ⋅⎜
0.023 ⋅ ⎜⎜
⎟ ⋅k
π ⋅ D ⋅ μ ⎟⎠ ⎝ k ⎠
⎝
h=
D
0.3
.
(19)
Once the physical dimensions of a heat exchanger have been established, h will
only vary based on fluctuations in the mass flow rate and the temperature. This
is shown by
h∝
m& 0.8 ⋅ cp(T )0.3 ⋅ k (T )0.7
μ (T )0.5
.
On a per kilogram basis Figure 9 shows the heat transfer coefficient’s
temperature dependence. The y-axis value is the product of the thermal
21
(20)
properties that are a function of temperature. The current operating temperature
of parabolic trough plants is below 400 °C due to the stability of the HTF. This
happens to be near the point of intersection where nitrate salt performs better
than Therminol VP-1™.
Heat transfer dependency on temperature
180
160
Product (mu,k,cp)
140
120
100
80
60
40
Product Therminol VP-1
20
Product Nitrate Salt
0
100
150
200
250
300
350
Temperature [C]
400
450
500
Figure 9: Heat transfer dependency on temperature per kg of fluid
Changes in the mass flow rate contribute significantly more to the heat
transfer coefficient. Figure 10 illustrates the h values for salt and oil at their
design flow rates. Nitrate salt is much larger due to the much higher flow rate, a
result of its lower specific heat. The mass flow rate approximation is a good first
22
order perturbation for the off-design conditions of the overall heat transfer
coefficient.
30000
Heat transfer dependency on temperature and design flow rate
Product (mu,k,cp,m)
25000
20000
15000
10000
Product Therminol VP-1
Product Nitrate Salt
5000
100
150
200
250
300
350
Temperature [C]
400
450
500
Figure 10: Heat transfer coefficients as products of variable components
If the heat transfer coefficient increases for a fluid then the overall heat
transfer coefficient, U will become larger. Assuming identical UA values for the
two fluids in a specific heat exchanger, a higher U value for one fluid implies a
smaller area.
23
CHAPTER 3
MODEL COMPONENTS
Weather Reader
Solar Field
Steam Train Heat Exchangers
Mixer
Turbine
Pressures
High
Pressure
Turbine
Reheater
Low
Pressure
Turbine
Power Out
Figure 11: Flow chart for power plant components
Weather Reader and Solar Field
The Weather Reader component, shown in Figure 11, is called first to
process weather conditions. Duffie & Beckman [16] describe the geometry of
24
tracking and sun angles based on local coordinates and Patnode [10] explicitly
solves them for a parabolic trough plant. Values were calculated for Las Vegas,
Nevada:
Longitude: - 115.08°
Latitude: 36.06 °N.
SCA length, spacing, focal length, and HCE values were used from Patnode
[10]. A solar field row is formed by a series of 4 SCA units and the heat transfer
fluid temperature increases incrementally over each SCA. Two rows are
connected in series to form a loop in the solar field. Increases in solar multiple
were calculated by increasing the number of loops in the solar field.
The total heat absorbed from the solar field is found by the calculation
Q& abs = DNI ⋅ cos(θ ) ⋅ IAM ⋅ RowShadow ⋅ EndLoss ⋅ η field ⋅ η HCE ⋅ SFAvail
(21)
The absorber tubes and HTF are hundreds of degrees Celsius above ambient
weather conditions and thermal losses are significant. The amount of energy
that can be actually be transferred from the solar field is called Q& collected and is
found by
Q& collected = Q& abs − Q& pipe _ loss − Q& receiver _ loss
(22)
The outlet temperature of the solar field, Tout , was assumed to be fixed at
390.56 °C. Inlet temperature, Tin , varied based on the last iteration and the mass
flow rate was solved;
m& =
Q& collected
.
c p (Tout − Tin )
25
(23)
Further details on the solar field can be found in the Matlab™ code in Appendix
A.
Heat Exchangers
A total of 10 distinct counter-flow shell and tube heat exchangers were
characterized and simulated in the three models. The method for solving the
unknowns in each heat exchanger differed depending on its position in the cycle.
With the exception of the preheater, every heat exchanger required solving the
heat transfer rate according to an energy balance and the effectiveness-NTU
method. The preheater calculation was simplified to only require an energy
balance.
The energy balance performed across the heat exchanger was solved using
m& 1 ⋅ cp1 ⋅ ΔT1 = m& 2 ⋅ cp 2 ⋅ ΔT2 .
(24)
Patnode [10] found inaccuracies by assuming an adiabatic heat exchanger
model. Heat loss through the heat exchangers was examined from adiabatic to
3% heat loss. At nominal power generation 3% heat loss in the heat exchangers
led to a 1 MW difference in power generation. Three percent heat loss was
chosen for all heat exchangers.
Design conditions for each heat exchanger not specified by the SEGS VI
design were established and an overall heat transfer coefficient, UA, was derived
to provide the necessary heat transfer. For each individual fluid, an energy
balance was used where
26
Q = m& ⋅ cp ⋅ ΔT ,
(25)
and a mass balances for each fluid was
m& in = m& out .
(26)
Once the heat transfer was determined, the design UA was solved by
UA =
Q
.
ΔTlm
(27)
The log mean temperature difference, ΔTlm , for a heat exchanger [17] is
expressed as
ΔTlm = (ΔTI ) − (ΔTII ) / ln(ΔTI / ΔTII ) ,
(28)
ΔTI = Th ,i − Tc ,i
(29)
ΔTII = Th , o − Tc , o .
(30)
where for counterflow
and
The inlet temperature and outlet temperature of the hot fluid and the inlet
temperature and outlet temperature of the cold fluid in the heat exchanger are
expressed by Th ,i , Th ,o , Tc ,i , Tc ,o , respectively.
27
Oil-Water Heat Exchangers
HTF
T5
T1
Superheater
T2
T6
Steam
Generator
T3
T7
Preheater
T8
T4
Water
Figure 12: Temperature assignments for the steam train
The mass flow rate of the HTF and T1, the HTF temperature entering the
steam train, shown in Figure 12, were known values. An optimization routine that
solved the state points for the steam generator and superheater was also written
to establish the mass flow rate of water across the steam generator. The water
mass flow rate set the pressure for the turbine entrance and pressure drop on the
working fluid side of the heat exchangers was neglected. Temperatures T6 and
28
T7 were assumed to be the saturation temperature set by the steam pressure.
The optimization routine minimized the energy difference between values
calculated for the energy balance and the effectiveness-NTU method. The UA
values shown in Table 1 were used as the design UA values for both the oilwater and the salt-water heat exchangers.
Table 1: UA values for steam train
Heat Exchanger
Superheater
Steam Generator
Reheater
UA
kW/°C
298
2051
653
Table 2 shows the design values for temperatures, pressures, and mass flow
rates presented by Lippke [8] and the results from this study. Temperatures refer
to the locations specified in Figure 12.
Table 2: Heat transfer design conditions for steam train heat exchangers
Kearney
Results
T1
°C
390.56
390.56
Kearney
Results
P initial
bar
103.42
100
P final
bar
100
100
m oil
kg/s
345.5
345.5
m water
kg/s
38.8
39.2
T2
°C
377.22
380.78
T3
°C
317.78
318.48
T4
°C
297.78
300.03
T5
°C
371
377.4
T6
°C
313.89
311.61
29
T7
°C
313.89
311.61
T8
°C
234.83
241.56
Once the mass flow rate of steam was determined, the design values for the
reheater, shown in Table 3, were solved by simultaneously solving the two heat
transfer equations. The flow rate for oil in the steam train was 87.2% of the total
HTF flow rate and 12.8% went to the reheater during all power generating
conditions.
Table 3: Reference conditions for reheater temperatures
Kearney
Results
T1
°C
390.56
390.56
T2
°C
297.78
287.4
T3
°C
208.67
205.17
T4
°C
371
367.89
P initial
bar
18.58
17.3
P final
bar
17.099
17.3
m oil
kg/s
50.9
50.68
m water
kg/s
33.04
33.28
Oil-Salt and Salt-Oil Heat Exchangers
The design flow rate for salt during charging and discharging was determined
by an energy balance that calculated enthalpy values for the temperature profile
shown in Table 4. Ts and To are the temperatures for the salt and oil,
respectively. The design charging flow rate for salt is equivalent to 2,350,800
kg/hr. The density of solar salt was calculated at 386°C to be 1844.5 m3/kg, so
the volumetric flow rate was found to be 1274.5 m3/hr. The amount of salt
needed for the Storage Oil-Water case will be equal to the number of hours of
storage times the hourly volumetric flow rate. Storage Salt-Water, however,
requires the number of hours of storage plus additional salt for operating the
30
plant. The amount of additional salt will depend on the cycle time through the
power block.
Table 4: Design conditions for oil-salt heat exchangers
Ts Hot
Ts Cold
To hot
To cold
flow rate
°C
°C
°C
°C
kg/s
Charging
386.00
293.00
393.00
299.00
396.00
Discharging
386.00
293.00
379.00
287.00
396.00
Q oil
flow rate salt
LMTD
UA
flow rate ratio
kJ/s
kg/s
°C
kW/°C
Salt/Oil
Charging
91231.71
653.38
6.49
14063.43
1.65
Discharging
87986.27
630.14
6.49
13563.14
1.59
Less heat can be transferred back to the oil due the temperature constraints. An
interesting consequence is that less salt is needed for discharging. The
difference in salt results in an extended discharging period for Storage Oil-Water
compared to Storage Salt-Water.
Salt-Water Heat Exchangers
The optimization code that was applied to the oil-water steam train was
applied to the salt-water steam train, where nitrate salt thermal properties
replaced oil thermal properties. Table 5 shows the design flow rate for steam is
36.23 kg/s, 3 kg/s less than the oil-water steam train. This decrease in flow rate
31
is reflected in the operating pressure which drops to 93.3 bar from 101 bar. Less
power is expected to be generated from the salt steam train. Additionally, the
turbine will experience more time in the saturation region due to the lower
pressure.
Table 5: Design conditions for molten salt steam train
Salt
Oil
T1
°C
386
390.56
T2
°C
375.74
380.78
T3
°C
314
318.48
T4
°C
298.47
300.03
T5
°C
372.83
377.4
T6
°C
305.8
311.61
Salt
Oil
T7
°C
305.8
311.61
T8
°C
237.05
241.56
P initial
bar
93.1
100
P final
bar
93.1
100
m oil
kg/s
569.4
345.5
m water
kg/s
36.2
39.2
Replacing synthetic oil with molten salt in the steam train heat exchangers
significantly affects the power block. A real plant with a molten salt steam train
may be designed differently than assuming the same arrangement. Nexant Inc.
[18] resolved this issue by modifying the design of the molten salt steam
generation system and their work is shown in Figure 13. The molten salt used in
the superheater and the reheater mix and together go to the steam generator.
Salt temperatures were higher than 390 °C, which is greater than the upper limit
of present HTF. Therefore their design values could not be extrapolated for this
32
study. In addition, their design cannot be readily compared to the SEGS VI
design because the power block would require modification.
HTF
HTF
T1
T5
T5
T1
Reheater
Superheater
T2
T6
Steam
From High
Pressure
Turbine
Steam
Generator
T3
T7
Preheater
T4
T8
Water
Figure 13: Representation of Nexant [17] molten salt steam train
Turbine
For all three power plant designs the turbine parameters were assumed to be
identical. The only variables that would change were the input values of inlet
temperature, pressure, water flow rate, and reheat inlet temperature. The salt
33
steam train is disadvantageous as a result because the turbine stages were built
for a higher pressure.
The steam enthalpy at the high pressure turbine inlet was determined by the
temperature and pressure solved in the superheater component. The enthalpy
for the low pressure turbine inlet was determined by the same method for the
reheater component. The inlet enthalpy for every other turbine stage was equal
to the enthalpy exiting the prior turbine stage. The outlet enthalpy was calculated
using the reference turbine stage efficiency and the isentropic relationship,
hout = hin − ε ⋅ (hin − hout _ isentropic )
(31)
A perturbation was included by Patnode [10] where efficiency reduces as a
function of steam mass flow rate.
ε decrease = 0.191 − 0.409 ⋅ (
m&
m& 2
) + 0.218 ⋅ (
)
m& ref
m& ref
ε = ε ref ⋅ (1 − ε decrease )
(32)
(33)
Adjusted design values for SEGS VI’s power block components can be found in
Lippke [8] and Patnode [10]. In solar literature, the mass flow rate and pressure
drop through a turbine stage can be expressed in a relationship with their
reference values. This is shown by
m&
P12 − P22
= 2
.
m& ref
P1ref − P22ref
(34)
Accordingly, once the back pressure from the condenser is known, the pressure
through the turbine can be back-calculated. However, Table 6 was tabulated by
34
equation 34 and shows the outlet pressure from the low pressure turbine does
not affect the inlet pressure to the high pressure turbine.
Table 6: Correlation of turbine inlet pressure and water mass flow rate
T amb = 0 °C
m water
kg/s
5
10
15
20
25
30
35
40
Pin HP1
bar
12.853
25.705
38.558
51.410
64.263
77.115
89.968
102.820
m water
kg/s
5
10
15
20
25
30
35
40
Pin HP1
bar
12.853
25.705
38.558
51.410
64.263
77.115
89.968
102.820
Pin LP5
Pin HP1/m water
bar
bar s / kg
0.037
2.5705
0.073
2.5705
0.108
2.5705
0.144
2.5705
0.180
2.5705
0.216
2.5705
0.252
2.5705
0.288
2.5705
T amb = 25 °C
Pin LP5
bar
0.060
0.086
0.118
0.151
0.186
0.221
0.256
0.291
Pin HP1/m water
bar s / kg
2.5705
2.5705
2.5705
2.5705
2.5705
2.5705
2.5705
2.5705
Variance in the lowest pressure turbine stage due to ambient weather conditions
does not affect the behavior of the high pressure turbine. Instead, the
relationship used in this model was
P = 2.57 ⋅ m& ,
35
(35)
where m& is the mass flow rate entering the high pressure turbine. This
relationship was also useful in the optimization code for the mass flow rate of
water in the steam train.
The power block model is a simplified version of the actual SEGS VI power
cycle. Heat exchangers and turbine stages were described individually however
models for the feedwater heaters, condensers, and cooling tower were not
implemented in to the full cycle. The work of the cooling tower and condenser
were assumed to cool the steam exiting the last stage of the turbine down to
seven degrees above ambient temperature. This was considered acceptable for
a dry cooling power plant. Further, the outlet pressure of the low pressure
turbine was determined to be the saturation pressure at this temperature
approximation.
Mixer and Power Plant Simplification
Two mixing units are utilized in both thermal storage designs. For the
Storage Oil-Water one unit mixes oil from the solar field with oil heated from
thermal storage. The second unit combines oil exiting the preheater, reheater,
and the oil used to charge the thermal storage tanks. The Storage Salt-Water
design utilizes a mixing unit with thermal storage discharge and another for
mixing the salt after cycling through the power block. The total mass in the mixer
is found by,
i
m& tot = ∑ m& i
1
36
(36)
where i is the number of streams entering the mixer. The resultant enthalpy of
the mixture is
i
hmix =
∑ m&
i
1
m& tot
(37)
⋅ hi
.
The cooling towers, condenser, feedwater heaters, and pumps were not
included in this model. The second assumption made was the preheater inlet
water temperature was a fixed the outlet water temperature. This value would be
found by modeling the series of 5 closed feedwater heaters, a pump, and the
open feedwater heater. Accurate parasitic calculations should be included in the
next modeling generation. This will include the modeling the missing
components and the power required to propagate the cycle.
Storage Tanks and Storage Controls Logic
The hot and cold storage tanks for Storage Oil-Water were identical with only
the temperature of salt varying. The Storage Salt-Water case required a cold
tank with an increased volume of one extra hour of salt. Each tank was assumed
to be fully mixed thermally. The fluid volume in the tank had the capability to
completely fill and discharge for every tank. The real limitations clarify that the
salt cannot fully discharge nor does it completely fill the tank [13]. For a desired
increase in thermal storage, the tank volume and area must increase.
The dimensions of the storage tank were meant to mimic the aspect ratio of
the Andasol One storage tanks [4]. Those dimensions were a 39 meter diameter
and a 19 meter tall tank. Above 11.7 meters the tank became conical, so the
37
height was approximated to be 11.7 meters. Power losses were reported 239 kW
and 259 kW lost for the cold tank and hot tank respectively. Given an area of
3823 m2, the heat loss terms can be expressed as 63 W/m2 and 67.7 W/m2. The
aspect ratio of the storage tanks diameter to height was preserved for resizing
the storage tanks to fit a 35 MWe plant. Table 7 displays the sizing requirements
for the storage tanks for the amount of hours in storage. The amount of mass is
the value calculated for the iteration interval of one second.
Table 7: Physical properties of thermal storage tanks
Salt Flow
Rate
m3/hr
1274.5
1274.5
1274.5
1274.5
1274.5
Discharge
Time
Hours
2
4
6
8
10
Volume
m3
2549
5098
7647
10196
12745
Diameter
m
22.045
27.77
31.79
34.99
37.7
Height
m
6.68
8.42
9.63
10.60
11.42
Area
m2
1226.03
1945.51
2549.55
3088.66
3585.62
Q Cold
Tank
MJ
1138.62
2277.24
3415.87
4554.49
5693.11
Mass
kg
1306
2612
3918
5224
6530
The energy balance for the mass of the tank was
M tan k = M tan k '+ m& in dt − m& out dt
(38)
where M tan k ' is the mass of the tank from the previous iteration. Heat into the
tank, Qin , and out of the tank, Qout , were solved by
Q = m& ⋅ cp ⋅ T
with T in absolute temperature in Kelvin. The heat in the tank was found by
38
(39)
Qtan k = Qin − Qout − Qloss
(40)
A 100 °C difference in Nitrate salt only affects its specific heat by one percent.
This error was considered negligible and the specific heat was treated as a
constant.
The temperature in the storage tank was found by determining the
temperature drop in the tank due to heat loss,
dT =
Qloss
M tan k ⋅ cp
(41)
and tank temperature was thus calculated at the end of the time step
Ttan k = Ttan k '− dT .
(42)
Heat loss and the associated temperature drop for an isolated 6 hour tank of
molten salt initially at 293 °C is shown in Figure 14. The heat loss term is based
on area of the tank and not the volume of salt so the linear behavior is expected.
Schulte-Fischedick [13] report the local solidification temperature for nitrate salt,
239 °C, is reached after 46 days for a half full tank with the capability of 7 hours
of storage. Local solidification was reached in the tank in Figure 14 after 42
days, which is within a reasonable range of the published study.
39
6 Hour Cold Tank, Half Full
300
290
Temperature [C]
280
270
260
250
240
230
220
210
200
0
200
400
600
800
1000
1200
Time [Hours]
Figure 14: Temperature loss in 6 Hour Cold Tank, half full
When the tank is only 20% full, local solidification occurs after 17 days. A
decreasing salt volume in one tank will yield more rapid temperature drop. A
more detailed model of the tanks will examine the heating requirements needed
for the hot tank and the cold tank because a minimum volume of salt must
remain in both tanks. Another concern is how much temperature decrease is
acceptable in the hot tank.
Other tank heat loss relations exist and could be explored. Discharging
molten salt from the hot tank is known to cause a decrease in temperature for the
remaining fluid in the hot tank to decrease. This is not only due to heat loss but
also of thermal stratification in the tank. Though not as extreme as a thermocline
40
storage system, stratification within each tank could be modeled in the next
generation of the code.
The basic thermal storage operating strategies for Storage Oil-Water and
Storage Salt-Water are shown in Figure 15 and Figure 16. Advanced thermal
storage controls will be valuable when parasitic calculations are analyzed. For
example, the minimum amount of hot salt discharge necessary to produce net
power could be determined.
Is flow rate less
than, greater than,
or equal to design
flow?
Oil flow
rate from
field
Equal:
Storage Dwells
Less Than:
Is there
Hot Salt?
Greater Than:
Is there Salt in
Cold Tank?
Yes:
Can salt meet
total oil demand?
Yes:
Can all of heat from
oil be used?
No:
Storage
Dwells
No:
Salt flow rate
is less than
max, all salt
is discharged
from Cold
Tank
Yes:
Max salt
flow rate is
discharged
from Cold
Tank
No:
Storage dwells
in Cold Tank
Yes:
Salt meets oil
demand and is
transferred from
Hot Tank to
Cold Tank
No:
Can salt
exchange help
make above
minimum
flow?
Yes:
All salt in Hot Tank
is discharged
No:
Storage dwells
both tanks
Figure 15: Storage Controls for Storage Oil-Water case
41
Oil flow
rate from
field
Calculate Field
Flow of salt in
oil-salt HX
Equal:
Hot Tank dwells
Cold Tank
discharges design
flow
Greater Than:
Is salt in Cold
Tank greater than,
less than, or equal
to Field Flow?
Greater or Equal:
Cold Tank discharges
design flow to PB and
sends Field Flow minus
design flow to Hot Tank
Less:
Cold Tank discharges
design flow to PB, sends
Cold Tank minus design
flow to Hot Tank, and
Field Flow is recalculated
Less:
Is Hot Tank plus
Field Flow
greater than min?
Yes:
Hot Tank fully
discharges and
mixes with Field
Flow
Is Field Flow less
than, greater than, or
equal to design flow?
No:
Is Field
Flow
above
min?
Less Than:
Is there Hot
Salt?
Yes: Does Hot
Tank have
greater, less, or
equal to design
flow minus Field
Flow?
Yes:
Cold Tank
discharges
Field Flow to
PB
No:
Field Flow
charges Hot
Tank
Equal:
Hot Tank fully
discharges, design
flow is sent to PB,
mixed temp
Greater: Hot
Tank discharges
difference from
design flow,
design flow is
sent to PB at
mixed T
No:
Field flow is
added to Hot
Tank
Figure 16: Storage controls for Salt-Water Storage
42
CHAPTER 4
RESULTS
No Storage
Three days were chosen to illustrate the behavior of the No Storage power
plant under varying weather and climactic conditions. The summer day chosen
was July 7th and it represents the ideal conditions for a solar parabolic trough
power plant. The Southwestern deserts are known for afternoon stormy
conditions in late summer. August 6th was chosen to represent a summer day
with typical cloud cover in the early afternoon. This day is particularly important
because of low solar radiation yet still a high demand for electricity, primarily due
to air conditioning. Winter conditions in Las Vegas are sunny, but the low
elevation of the sun increases reflection losses and will decrease the amount of
energy that can be absorbed by a parabolic trough power plant because it is a
single axis tracking technology.
43
July 7: Power Generation
200
Q DNI
Q Absorbed
Q Collected
Gross Power
180
160
Gross Power [MW]
140
120
100
80
60
40
20
0
0
5
10
15
20
Time [Hour of Day]
Figure 17: Hourly power totals for July 7, a typical sunny day
Figure 17 shows that energy generation on a clear summer day remains
steady through out the day. Power generation is delayed in the morning and
evening partially due to the troughs not tracking within ten degrees above the
horizon. The difference between the energy absorbed and the energy collected
is due to thermal losses in the solar field.
44
August 6: Power Generation
180
Q DNI
Q Absorbed
Q Collected
Gross Power
160
Gross Power [MW]
140
120
100
80
60
40
20
0
0
5
10
15
20
Time [Hour of Day]
Figure 18: Hourly power totals for August 6, a day with afternoon clouds
The model demonstrates accurate reflection of the ambient weather
conditions in Figure 18, when clouds arise at noon. Power generation is
significantly reduced by low DNI in the early afternoon, yet the slope of gross
power is not as steep as the slope of the solar field outputs.
45
December 1: Power Generation
180
Q DNI
Q Absorbed
Q Collected
Gross Power
160
Gross Power [MW]
140
120
100
80
60
40
20
0
0
5
10
15
20
Time [Hour of Day]
Figure 19: Hourly power totals for December 1st, a clear winter day.
Despite the high solar radiation, Figure 19 shows less energy is absorbed by
the solar field in winter due to reflection losses due of the incidence angle.
Two acceptable methods of increasing annual energy generation for a given
power block size are to increase the solar multiple or to add thermal storage. An
actual plant is not likely to incorporate thermal storage after it is built but it is
possible for a plant to increase the size of its solar field.
An increase in solar multiple is not beneficial for the entire year. Figure 20
illustrates that all solar multiple values reach maximum power generation on July
46
7th. Potential thermal energy is wasted during the summer months even for a
solar multiple of one. However, the revenue lost by wasting potential power must
be compared to the cost of implementing thermal storage. A solar multiple of
one will not waste enough potential power to justify thermal storage. The solar
multiple has to increase for thermal storage to be a significant contributing factor
to the plant.
July 7: No Storage, Varying Solar Multiple
40
SM 2
SM 1.8
SM 1.6
Gross Power [MW]
35
30
SM 1.4
SM 1.2
25
SM 1
20
15
10
5
0
0
5
10
15
20
Time [Hour of Day]
Figure 20: Gross power generation for July 7 with several solar field sizes
47
Additionally, the simulation confirmed that at SM 1.6 the mass flow rate
exceeded double the design flow rate. This signifies more oil-salt heat
exchanger area is needed for solar multiples greater than 1.6.
August 6: No Storage, Varying Solar Multiple
40
35
Gross Power [MW]
30
SM 2
25
SM 1.8
20
SM 1.6
SM 1.4
15
SM 1.2
SM 1
10
5
0
0
5
10
15
20
Time [Hour of Day]
Figure 21: Gross power generation for August 6 with several solar field sizes
48
The solar field size becomes more relevant for a summer day that becomes
cloudy, such as August 6th, presented in Figure 21. The solar multiples greater
than one waste more potential thermal energy in the morning but aid in
maintaining higher power generation during the cloudy period.
December 1: No Storage, Varying Solar Multiple
40
35
Gross Power [MW]
30
25
20
SM 2
SM 1.8
SM 1.6
SM 1.4
SM 1.2
SM 1
15
10
5
0
0
5
10
15
20
Time [Hour of Day]
Figure 22: Gross power generation for Dec 1 with several solar field sizes
49
The overall trend in Figure 22 shows significant improvement in power
generation by augmenting the solar field size. The data point at 1 PM for the SM1
curve in is inconsistent with the other solar field sizes. The discrepancy is due to
a sensitivity issue in the steam generation optimization routine that only occurs
when the oil mass flow rate is in the range of 40-80 kg/s. A secondary
convergence criterion should be explored for the optimization routine.
Power versus Water Mass Flow Rate
40
35
Power [MWe]
30
25
20
15
10
July 7
5
Aug 6
Dec 1
0
0
5
10
15
20
25
30
35
40
Water Mass Flow Rate [kg/s]
Figure 23: Power versus water mass flow rate for the No Storage case
50
According to Figure 23, for SM 1 without storage, power generation appears
to be linearly related to water mass flow rate. A linear regression could be
developed to simplify the calculations for the power block. However, the heat
exchanger equations would still have to be calculated for the balance of the
plant. Or, the regression would have to include the inlet temperature of the hot
fluid in steam generation as an input and the hot fluid outlet temperature as an
output.
The optimization code written to determine the mass flow rate of the water is
dependent on the inlet heat transfer fluid temperature. A decrease in the quality
of the heat transfer fluid temperature will decrease the water flow rate. Therefore
the temperature exiting thermal storage will contribute to the amount power
generated.
51
Storage Oil-Water Results
Storage Oil-Water: July 7, 4 hours
40
SM 2
SM 1.8
35
SM 1.6
SM 1.4
30
Gross Power [MW]
SM 1.2
SM 1
25
20
15
10
5
0
0
5
10
15
20
Time [Hours]
Figure 24: July 7th with four hours of thermal storage, varying solar multiple
The power generated after 6 PM in Figure 24 represents the expected
behavior of the power generated from thermal storage. The decrease in power is
due to the HTF temperature drop from the increased number of heat exchangers.
52
Storage Oil-Water: August 6, 4 hours
40
SM 2
SM 1.8
35
SM 1.6
SM 1.4
30
Gross Power [MW]
SM 1.2
SM 1
25
20
15
10
5
0
0
5
10
15
20
Time [Hours]
Figure 25: Aug 6th with four hours of storage, varying solar multiple
Four hours of thermal storage and SM 1.4 or greater will provide enough
thermal energy in Figure 25 to overcome the cloudy weather for August 6th. At 1
PM thermal storage is discharged and the solar multiples of 1 and 1.2 did not
have enough thermal storage to generate power at full capacity during the
transient period. The increase in power generation at 5 PM is due to DNI
returning to high values. The larger the solar multiple the longer into the evening
53
storage can provide power. Both SM 1.8 and SM 2 are able to full charge the
four hour tanks.
Storage Oil-Water: December 1, 4 hours
40
SM 2
SM 1.8
35
SM 1.6
SM 1.4
30
Gross Power [MW]
SM 1.2
SM 1
25
20
15
10
5
0
0
5
10
15
20
Time [Hours]
Figure 26: Dec 1st with four hours of storage, varying solar multiple
Despite doubling the solar field size, Figure 26 illustrates that some winter
days will not be able to utilize thermal storage. Too many consecutive days with
similar conditions will require the use of auxiliary heating for the storage tanks.
54
There are clear differences between power generated by No Storage and
Storage Oil-Water. While the increase in solar multiple aids the No Storage
case, the value of an increase is more evident when thermal storage is
implemented. The balance between the amount of storage and the size of the
solar field is critical for cost analysis and power generation. The most cost
effective solution will also depend on the location.
As the solar multiple and amount of storage increases the ability to produce
power for longer hours continues to rise. The longest amount of thermal storage
explored was 10 hours and Figure 27 demonstrates the results for July 7th. At
SM 1.6 and above 24 hour power generation is achievable.
55
Storage Oil-Water: July 7, 10 hours
40
35
Gross Power [MW]
30
25
20
15
SM 2
SM 1.8
10
SM 1.6
SM 1.4
5
SM 1.2
SM 1
0
0
5
10
15
20
Time [Hours]
Figure 27: July 6th with ten hours of storage, varying solar multiple
This is realistic because SM 1 can collect 120% of the design thermal energy
from the solar field when DNI reaches 1000 W/m². At SM 1.6 the thermal energy
from the solar field will double design conditions, so for every hour of high solar
insolation an hour of thermal storage can also be harvested. Power generation
without thermal storage ceases at 8 PM. Thermal storage begins is fully utilized
from 8 PM until 6 AM, a total of 10 hours. Due to some thermal storage utilized
at 7 PM, the amount of thermal storage at 6 AM is less than full capacity. The 10
hours of thermal storage was found to be the minimum amount of storage to
provide 24 hour electricity production.
56
Storage Oil-Water: August 6, 10 hours
40
SM 2
SM 1.8
35
SM 1.6
SM 1.4
Gross Power [MW]
30
SM 1.2
SM 1
25
20
15
10
5
0
0
5
10
15
20
Time [Hours]
Figure 28: Aug 6th with ten hours of storage, varying solar multiple
The results for ten hours of thermal storage during a cloudy summer day,
depicted in Figure 28, are similar to those of four hours of thermal storage.
However, the total energy generation for the day is highly dependent on the solar
field size.
57
Monthly Gross Energy Output: No Storage
14000
Gross Energy Generation [MWh]
SM 1
12000
SM 1.4
SM 1.6
10000
SM 2
8000
6000
4000
2000
0
Jan
Feb
Mar
Apr
May June
July
Aug
Sep
Oct
Nov
Dec
Month of Year
Figure 29: Monthly gross energy output for the No Storage Case
The trends of gross energy generation by month are shown in Figure 29. An
increase in solar field area improves generation all year but is most important for
a plant without storage during the non-summer months.
58
Monthly Gross Energy Output: 8 hours
Gross Energy Generation [MWh]
20000
SM 1
18000
16000
SM 1.4
SM 1.6
14000
SM 2
12000
10000
8000
6000
4000
2000
0
Jan
Feb
Mar
Apr
May June July
Aug
Sep
Oct
Nov
Dec
Month of Year
Figure 30: Monthly gross energy output for Storage Oil-Water with 8 hour tank.
The appreciable amount of energy that can be generated when storage is
incorporated into the plant is evident in Figure 30. There is an increase of 1,000
MWh even for the SM 1 case during the summer months. For the SM 2 case,
the increase is 7,000 MWh above the No Storage design.
59
Monthly Gross Energy Output: SM 1.4
Gross Energy Generation [MWh]
18000
No Storage
4 hours
16000
6 hours
8 hours
14000
12000
10000
8000
6000
4000
2000
0
Jan
Feb
Mar
Apr
May June
July
Aug
Sep
Oct
Nov Dec
Month of Year
Figure 31: Monthly gross energy output for solar multiple of 1.4
Winter conditions clearly level the benefit of thermal storage, as seen in
Figure 31. For a 1.4 solar multiple the differences in energy production from
varied storage tanks size are only appreciable from May to August.
60
Comparison of Storage Designs
Comparing Storage Cases: July 7, SM 1.6, 4 hours
40
Storage Oil-Water
Storage Salt-Water
35
Gross Power [MW]
30
25
20
15
10
5
0
0
5
10
15
20
Time [Hours]
Figure 32: Storage designs for July 7, SM 1.6 and 4 hours of storage
The differences between the two thermal storage designs, shown by Figure
32, are very evident. The lower design flow rate for steam in the Storage SaltWater case results in less power generation during normal operating hours.
Also, the Storage Salt-Water case generates more power when the thermal
storage provides the only heat source and the amount of power does not
61
decrease during discharging because the number of heat exchangers remains
constant. However, this increase in power production from storage discharging
is less than the power not produced during normal operating hours.
Additionally, the Storage Oil-Water design produces more power at the end of
the day for two reasons. Less salt is needed for thermal discharging, which will
extend hours of operation. However the more dominant cause is the amount of
heat loss in the oil-salt heat exchangers. The three percent heat loss becomes
a much larger amount when all HTF from the solar field transfers thermal energy
into the molten salt.
62
Comparing Storage Cases: July 7, SM 2, 10 hours
40
35
Gross Power [MW]
30
Storage Oil-Water
25
Storage Salt-Water
20
15
10
5
0
0
5
10
15
20
Time [Hours]
Figure 33: Storage designs for July 7, SM 2 and 10 hours of storage
The trend of longer power generation by Storage Oil-Water is more obvious in
Figure 33, where the solar multiple increased to 2 and the storage tanks contain
10 hours of thermal storage. While Storage Oil-Water can provide 24 hours of
power, Storage Salt-Water cannot. Increasing the solar multiple and the number
of hours of storage will not favor Storage Salt-Water for this operating strategy.
63
Comparing Storage Cases: August 6, SM 1.6, 4 hours
40
Storage Oil-Water
Storage Salt-Water
35
Gross Power [MW]
30
25
20
15
10
5
0
0
5
10
15
20
Time [Hours]
Figure 34: Storage designs for August 6, SM 1.6 and 4 hours of storage
Storage designs are compared for August 6th in Figure 34 and the power
plants have enough thermal energy smooth over the transient afternoon weather
conditions. At 1 PM thermal storage is discharged and Storage Oil-Water
displays a decrease in power generation. However, because of a moderate level
of DNI thermal storage is not needed to discharge at full capacity. During the
afternoon transient hours, power production from Storage Oil-Water does not
decrease below Storage Salt-Water power production levels.
64
Comparing Storage Cases: Dec 1, SM 1.6, 4 hours
40
Storage Oil-Water
35
Storage Salt-Water
Gross Power [MW]
30
25
20
15
10
5
0
0
5
10
15
20
Time [Hours]
Figure 35: Storage designs for Dec 1, SM 1.6 and 4 hours of storage
The two curves in Figure 35 display the same trend for the winter conditions.
Storage Salt-Water generates less power than Storage Oil-Water during offdesign conditions. However, the molten salt is continuously cycled in Storage
Salt-Water. This reduces the concern for solidification of the molten salt and will
also reduce the amount of auxiliary heating needed, especially for low solar
multiples.
65
The annual energy totals for the solar field and gross power generation are
presented for the No Storage case in Table 8. An increase in solar multiple is
followed by an increase in gross energy production, however the increase is nonlinear.
Table 8: Annual energy totals for No Storage
No Storage
Incident
Absorbed
Collected
SM
1
1.2
1.4
1.6
1.8
2
MWhth
471721
566065
660409
754753
849097
943441
MWhth
256398
307678
358958
410237
461517
512797
MWhth
215960
258510
301038
343574
386079
428614
Gross Energy Production
MWhe
81044
90572
97046
101904
105649
108586
(factor of SM1)
1.00
1.12
1.20
1.26
1.30
1.34
Table 9 shows the annual energy generation for each storage case examined
divided by the annually energy of the No Storage case at solar multiple of one.
This normalization neutralizes most operating assumptions and allows all annual
energy totals to be compared to the relative performance of the bases case.
When a plant incorporates thermal storage the rate of gross annual energy
production is accelerated. Storage sizes greater than 4 hours are not useful for
Storage Oil-Water at SM lower than 1.4 and for Storage Salt-Water at SM lower
than 1.6. Tank heat loss even neutralizes the benefits of additional power
production in some of these cases.
66
The same amount of energy is produced for Storage Oil-Water cases of SM
1.8 with 4 hours of storage and SM 1.6 with 6 hours of storage. Net power
produced and an economic analysis of the cases would determine which
condition will provide a better solution.
Accurate parasitic calculations will require several calculations not performed
in the No Storage plant. The Storage Oil-Water design will need additional HTF
pumping, salt pumping power between tanks, and auxiliary heating requirements.
The storage Salt-Water design will require the pumping power for molten salt
through the steam train and reheater, and auxiliary heating.
According to Table 9, Storage Salt-Water never produces the power that can
be obtained from Storage Oil-Water. However, there are alternative operating
strategies that highlight the advantages of Storage Salt-Water such as shifting
power generation [19].
67
Table 9: Normalized annual energy generation
Storage Oil-Water
SM
1
1.2
1.4
1.6
1.8
2
No Store
1.00
1.12
1.20
1.26
1.30
1.34
2h
1.04
1.22
1.33
1.42
1.49
1.54
4h
1.04
1.27
1.43
1.55
1.64
1.71
6h
1.05
1.28
1.49
1.64
1.75
1.85
8h
1.04
1.27
1.50
1.70
1.85
1.96
10 h
1.04
1.27
1.50
1.73
1.91
2.05
Storage Salt-Water
SM
1
1.2
1.4
1.6
1.8
2
No Store
1.00
1.12
1.20
1.26
1.30
1.34
2h
0.96
1.13
1.24
1.32
1.38
1.43
4h
0.96
1.17
1.32
1.43
1.52
1.58
68
6h
0.96
1.17
1.37
1.52
1.63
1.71
8h
0.96
1.17
1.38
1.57
1.71
1.82
10 h
0.96
1.17
1.38
1.59
1.76
1.90
CHAPTER 5
CONCLUSIONS AND RECOMMENDATIONS
Matlab™ code was successfully written to simulate the gross power output for
three solar parabolic trough power plant designs: No Storage, Storage Oil-Water,
and Storage Salt-Water. The primary design parameters were extrapolated from
SEGS VI, when applicable. The model behaves as expected to weather and
seasonal changes. It deviates from SEGS VI’s power output due to
simplifications and differing operating strategies. The analysis of the competing
thermal storage designs is valid as all three plant designs are compared on equal
footing.
Several performance distinctions were identified between the two tank indirect
thermal storage systems. Storage Oil-Water displayed a lower power output
when thermal storage was the primary heat source. However, Storage SaltWater did not produce as much power during normal operating conditions. This
was due to a lower design temperature of salt at the power block heat
exchangers entrance and also because nitrate salt has a lower heat capacity
than synthetic oil. For the basic operating strategy examined, to maximize the
amount of time operating at full-capacity, Storage Oil-Water showed better
annual gross energy generation for all solar multiples and storage tank sizes.
A significant cost increase to Storage Salt-Water is the size of the oil-salt heat
exchanger. Additionally, this increase in size led to greater heat loss when
transferring thermal energy from oil to salt. However, the assumption that both
69
heat transfer fluids maintained identical UA values for the steam generation heat
exchangers implies the Storage Salt-Water heat exchanger area will decrease.
This will reduce the cost of the Storage Salt-Water unit. Auxiliary heating
equipment will be necessary for both storage designs; however their presence in
the Storage Salt-Water case is only a safety precaution because the salt is
cycled daily.
The size of the storage tanks and the quantity of molten salt were identified.
It was also determined that the volume of salt needed in Storage Salt-Water will
increase to include the amount needed for the power block loop. Further
analysis can also include component cost analysis, such as size of solar field and
hours of thermal storage, that will help determine the most cost-effective plant for
a desired annual energy generation total.
Parasitic calculations can be performed in the future to calculate the net
annual power and to provide clear annual solar-to-electric efficiency values.
Several parasitic relationships need to be identified including salt pumping
requirements for both storage designs and auxiliary heating requirements.
Pumping power will increase with the molten salt steam train due to a higher flow
rate and a higher viscosity.
The optimization scheme used to solve the mass flow rate of the cooling fluid
in the heat exchanger problems could use improvement, as evidence in the
variability at low mass flow rates. Secondary convergence criteria could be
explored. The alternate design for molten salt steam generation performed by
70
Nexant [18] would lead to a new power block optimization. This may improve the
power generating capabilities of the Storage Salt-Water design.
Further operating strategies could modify storage controls to shift power
generation to match peak demand hours. This would be desired by utility
companies and they are likely to pay more for power produced during peak load
demand. Shifting power generation may favor Storage Salt-Water because
thermal storage will be utilized as the primary heat source for a greater amount of
time.
71
APPENDIX A
MATLAB CODE
%Storage Salt-Water: SM 1, 4 hours storage
% JK 2009
%Inputs
Data=xlsread('Las_Vegas_TMY3.xls');
Day=Data(:,1);
Hour=Data(:,2);
DNI=Data(:,3);
Tamb=Data(:,4);
WindSpeed=Data(:,5);
%Location Parameters
Long_L=115.08;
Long_St=120;
Lat=36.06;
phi=Lat*pi/180;
beta=0;
gamma=0; gamma_s=1;
%Local Longtitude
%Standard Longitude, GMT -8
%Local Latitude
%Latitude in radians
%Slope from horizontal
%Surface azimuth angle... sine(0)=0
%Solar Field Parameters
%Units are m and m^2
L_SCA_loop=753.6;
%Length of Solar Collector Assembly
L_SCA=50;
%Length of single collector
L_spacing=15;
%Spacing between troughs
Num_SCA=50*1;
%Number of SCAs
W_SCA=4.83;
%Width of Luz2 SCA
SolarArea=L_SCA_loop*W_SCA*Num_SCA; %Solar Area
Loops=Num_SCA/2;
%Loops treat hot and cold row
FocalLength = 5;
%Focal Length of Trough
T_f_o = 390.56;
h_field_out=1000*(-18.34+1.498*T_f_o+0.001377*T_f_o^2); %[J/kg]
mdotField_ref = 396;
%Heat Collection Element Parameters
72
etaField=0.994*0.98*0.935*0.95; %Eta Field = TrkTwstErr * GeoAcc *…
MirRef * MirCln
etaHCE=0.98*0.99*0.963*0.95*0.96;
%Eta HCE = HCEdues *…
BelShad*…EnvTrans * HCE abs * HCEEmics
SolarAvailability=0.99;
%Coefficients for receiver heat loss
A0=-9.463;
A1=3.030e-1;
A2=-1.387e-3;
A3=6.929e-6;
B0=7.650e-2;
B1=1.129e-7;
%Heat Exchanger Parameters
UA_SH=298000;
UA_SG=2051000;
UA_pre = 752000;
%Storage Parameters
TankAreaC = 2121.67;
TankAreaH = TankAreaC;
MassStorageC_initial = 3265;
Q_ColdTank_initial = 2846555093;
T_ColdTank_initial = 293;
MassStorageH_initial = 0;
Q_HotTank_initial = 0;
T_HotTank_initial = 0;
for i=1:8760
%Solar Field inlet temperature
if i==1
T_f_i(i,1)=297;
else
T_f_i(i,1)=T_o_out(i-1);
end
%Weather Reader -- Reads weather and serves as Solar Field part I
73
[Q_abs(i,1)] = WeatherReader(Long_St,Long_L,phi,L_spacing,
W_SCA,FocalLength,L_SCA_loop,L_SCA,etaField,
etaHCE,SolarAvailability,SolarArea,Day(i), Hour(i), DNI(i), Tamb(i),
WindSpeed(i),i);
%Solar Field Calculations
if Q_abs(i)<=0
mdot_field(i,1)=0;
Qdot_collected(i,1)=0;
Qdot_collected_MW(i,1)=0;
Qdot_absorbed_MW(i,1)=0;
else
[mdot_field(i,1), Qdot_collected(i,1), Qdot_collected_MW(i,1),
Qdot_absorbed_MW(i,1)] = SolarField…
(T_f_i(i),T_f_o,A0,A1,A2,A3,B0,B1,DNI(i),Tamb(i),Q_abs(i),SolarArea,…
h_field_out );
end
%Solar Field cumulative values
FieldRatio(i,1)=mdot_field(i)/mdotField_ref;
Q_Total_Incidence_MW(i,1)=DNI(i)*SolarArea/1000000;
%Initiate Thermal Storage
if i ==1
MassStorageC(i,1) = MassStorageC_initial;
Q_ColdTank(i,1) = Q_ColdTank_initial;
T_ColdTank(i,1) = T_ColdTank_initial;
MassStorageH(i,1) = 0;
Q_HotTank(i,1) = 0;
T_HotTank(i,1) = 0;
else
MassStorageC(i,1) = MassStorageC(i-1);
Q_ColdTank(i,1) = Q_ColdTank(i-1);
T_ColdTank(i,1) = T_ColdTank(i-1);
MassStorageH(i,1) = MassStorageH(i-1);
Q_HotTank(i,1) = Q_HotTank(i-1);
T_HotTank(i,1) = T_HotTank(i-1);
end
74
[T_o_out(i,1),mdot_s(i,1), T_salt_to_PB(i,1), mdot_to_PB(i,1), T_HotTank(i,1),
MassStorageH(i,1),Q_HotTank(i,1),T_HotTank_toHX(i,1),dT(i,1)] =
StorageControlsSalt(mdot_field(i),T_ColdTank(i),TankAreaH, MassStorageH(i),
Q_HotTank(i), T_HotTank(i),MassStorageC(i));
%Divide Field Flow into steam train and reheat
mdot_h_sh(i,1) = 0.872*mdot_to_PB(i);
mdot_h_rh(i,1) = 0.128*mdot_to_PB(i);
%Turn power plant on if power is greater than 3 MW -->66kg/s Field Flow
if mdot_to_PB(i)<66
T2(i,1)=0;
T3(i,1)=0;
T4(i,1)=0;
T5(i,1)=0;
T6(i,1)=0;
T8(i,1)=0;
Qpre(i,1)=0;
Qsh(i,1)=0;
Qsg(i,1)=0;
P(i,1)=0;
mdot_w(i,1)=0;
T_out_HP2(i,1)=0;
h_out_HP2(i,1)=0;
Pout_HP2(i,1)=0;
T_w_rh_out(i,1)=0;
T_htf_rh_out(i,1)=0;
h_rh_diff(i,1)=0;
W_HP1(i,1)=0;
W_HP2(i,1)=0;
W_LP1(i,1)=0;
W_LP2(i,1)=0;
W_LP3(i,1)=0;
W_LP4(i,1)=0;
W_LP5(i,1)=0;
T_to_exp(i,1)=0;
T_to_ColdTank(i,1)=0;
mdot_to_ColdTank(i,1)=0;
else
%Heat Exchanger Steam Train
[T2(i,1), T3(i,1), T5(i,1), T6(i,1), Qsh(i,1), Qsg(i,1), P(i,1), mdot_w(i,1)] =
…
75
f_main_search_salt(T_salt_to_PB(i),mdot_h_sh(i),UA_SH, UA_SG);
[T4(i,1), T8(i,1), Qpre(i,1)] = Preheater_salt(mdot_h_sh(i),mdot_w(i),…
P(i),T3(i),T6(i));
% Calculate turbine pressures from mass flow rate
[Pout_LP5 Pout_LP4 Pout_LP3 Pout_LP2 Pin_LP1 Pout_LP1
Pout_HP2(i,1) Pin_HP1 Pout_HP1...
mdot_LP5,mdot_LP4,mdot_LP3,mdot_LP2,mdot_LP1,mdot_HP2,…
mdot_HP1]…= TurbinePressure (mdot_w(i),Tamb(i));
% High Pressure Turbine
[W_HP1(i,1) W_HP2(i,1) T_out_HP2(i,1) h_out_HP2(i,1)] =…
Turbine_HP…
(T5(i), Pin_HP1, Pout_HP1, mdot_HP2, mdot_HP1, Pout_HP2(i));
% Reheater Calculations
[T_htf_rh_out(i,1), T_w_rh_out(i,1)]= Reheater_salt(mdot_LP1,…
Pout_HP2(i), T_salt_to_PB(i),mdot_h_rh(i),h_out_HP2(i));
% Low Pressure Turbine
[W_LP1(i,1) W_LP2(i,1) W_LP3(i,1) W_LP4(i,1) W_LP5(i,1)] =…
Turbine_LP (T_w_rh_out(i), Pin_LP1, Pout_LP1, Pout_LP2, …
Pout_LP3, Pout_LP4, Pout_LP5,
mdot_LP5,mdot_LP4,mdot_LP3,mdot_LP2,mdot_LP1);
%h_rh_diff(i,1) = h_out_HP2(i) - XSteam('h_px',Pout_HP2(i),1);
% Salt Mixer
[T_to_ColdTank(i,1),mdot_to_ColdTank(i,1)] = Mixer_salt…
(mdot_h_sh(i), mdot_h_rh(i),T4(i),T_htf_rh_out(i));
end
%Mass and Energy Balance on Cold Tank
[Q_ColdTank(i,1),T_ColdTank_toHX(i,1),T_ColdTank(i,1),MassStorageC(i,1)]
= ColdTank2(TankAreaC, MassStorageC(i),Q_ColdTank(i), T_ColdTank(i),
mdot_to_ColdTank(i), mdot_s(i),T_to_ColdTank(i));
%Calculate Power
[WelectricMW(i,1), Welectric(i,1)] = Generator(W_LP1(i), W_LP2(i),…
W_LP3(i), W_LP4(i), W_LP5(i), W_HP1(i), W_HP2(i));
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end
Storage_Mass_Balance =[MassStorageC+MassStorageH];
KeyParameters=[Q_Total_Incidence_MW,Qdot_absorbed_MW,Qdot_collected_
MW,WelectricMW,mdot_w,MassStorageH,T_HotTank,Q_HotTank,MassStorage
C,T_ColdTank,Q_ColdTank,mdot_to_PB,a];
xlswrite('Results_StoreSalt_4h_SM1_', KeyParameters, 'sheet1','A1');
function [T_o_out,mdot_s,
T_salt_to_PB,mdot_to_PB,T_HotTank,MassStorageH,…
Q_HotTank,T_HotTank_toHX,dT ] = StorageControlsSalt(mdot_field,…
T_ColdTank,TankAreaH, MassStorageH,Q_HotTank,
T_HotTank,MassStorageC)
% StorageControlSalt dictates how to charge, discharge, and dwell storage
tanks.
% JK 2009
% mdot_s exits MassStorageC
% mdot_to_PB goes to PB;
%Calculate salt flow rate from solar field ~ Field Flow
[T_o_out, mdot_s]= f_Storage_Charger_salt(mdot_field,T_ColdTank);
mdot_s = round(mdot_s);
T_salt_to_PB = 386;
mdot_o = mdot_field;
if mdot_s == 653
mdot_s_in_H = 0;
mdot_s_out_H = 0;
mdot_to_PB = 653;
[T_HotTank,MassStorageH,Q_HotTank,T_HotTank_toHX,dT] = HotTank…
(TankAreaH, MassStorageH, Q_HotTank, T_HotTank, mdot_s_in_H,
mdot_s_out_H);
elseif mdot_s > 653
%Does Cold Tank have enough to discharge entire flow?
if MassStorageC >= mdot_s
mdot_charge = mdot_s - 653;
mdot_to_PB = 653;
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mdot_s_in_H = mdot_charge;
mdot_s_out_H = 0;
[T_HotTank,MassStorageH,Q_HotTank,T_HotTank_toHX,dT] = HotTank…
(TankAreaH, MassStorageH, Q_HotTank, T_HotTank, mdot_s_in_H,…
mdot_s_out_H);
else
mdot_charge = MassStorageC - 653;
mdot_to_PB = 653;
mdot_s = MassStorageC;
T_salt_in=T_ColdTank;
[T_o_out mdot_o] = f_Storage_Charger_salt2oil(mdot_s,T_salt_in);
mdot_s_in_H = mdot_charge;
mdot_s_out_H = 0;
[T_HotTank,MassStorageH,Q_HotTank,T_HotTank_toHX,dT] = HotTank…
(TankAreaH, MassStorageH, Q_HotTank, T_HotTank, mdot_s_in_H,…
mdot_s_out_H);
end
else
if MassStorageH <=0
if mdot_s <= 66
mdot_charge = mdot_s;
mdot_s_in_H = mdot_charge;
mdot_s_out_H = 0;
mdot_to_PB = 0;
[T_HotTank,MassStorageH,Q_HotTank,T_HotTank_toHX,dT] =
HotTank…
(TankAreaH, MassStorageH, Q_HotTank, T_HotTank, mdot_s_in_H,…
mdot_s_out_H);
else
mdot_to_PB = mdot_s;
mdot_s_in_H = 0;
mdot_s_out_H = 0;
[T_HotTank,MassStorageH,Q_HotTank,T_HotTank_toHX,dT] =
HotTank…
(TankAreaH, MassStorageH, Q_HotTank, T_HotTank, mdot_s_in_H,…
mdot_s_out_H);
end
else
78
mdot_needed = 653 - mdot_s;
if MassStorageH == mdot_needed
mdot_discharge = mdot_needed;
mdot_s_in_H = 0;
mdot_s_out_H = mdot_discharge;
[T_HotTank,MassStorageH,Q_HotTank,T_HotTank_toHX,dT] =
HotTank…
(TankAreaH, MassStorageH, Q_HotTank, T_HotTank, mdot_s_in_H,…
mdot_s_out_H);
%mix field plus storage
[T_salt_to_PB,mdot_to_PB] = Mixer_salt2(mdot_s,mdot_discharge,…
T_HotTank_toHX);
elseif MassStorageH > mdot_needed
mdot_discharge = mdot_needed;
mdot_s_in_H = 0;
mdot_s_out_H = mdot_discharge;
[T_HotTank,MassStorageH,Q_HotTank,T_HotTank_toHX,dT] =
HotTank…
(TankAreaH, MassStorageH, Q_HotTank, T_HotTank, mdot_s_in_H,…
mdot_s_out_H);
%mix field plus storage
[T_salt_to_PB,mdot_to_PB] = Mixer_salt2(mdot_s,mdot_discharge,…
T_HotTank_toHX);
else
mdot_capable = MassStorageH + mdot_s;
if mdot_capable >= 66
mdot_discharge = MassStorageH;
mdot_s_in_H = 0;
mdot_s_out_H = mdot_discharge;
[T_HotTank,MassStorageH,Q_HotTank,T_HotTank_toHX,dT] =
HotTank…
(TankAreaH, MassStorageH, Q_HotTank, T_HotTank, mdot_s_in_H,…
mdot_s_out_H);
%mix field plus storage
[T_salt_to_PB,mdot_to_PB] = Mixer_salt2(mdot_s,mdot_discharge,…
T_HotTank_toHX);
else
mdot_charge = mdot_s;
mdot_s_in_H = mdot_charge;
mdot_s_out_H = 0;
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[T_HotTank,MassStorageH,Q_HotTank,T_HotTank_toHX,dT] =
HotTank (TankAreaH, MassStorageH, Q_HotTank, T_HotTank, mdot_s_in_H,
mdot_s_out_H);
%mix field plus storage
mdot_to_PB = 0;
end
end
end
end
function [T_o_out mdot_s] = f_Storage_Charger_salt(mdot_surplus,T_salt_in)
% f_Storage_Charger_salt calls the optimization routine Oil-Salt HX
% JK 2009
mdot_o = mdot_surplus;
if mdot_o < 4
mdot_s = mdot_o*1.6;
if mdot_s ==0
T_o_out = 0;
else
%oil temp is
T_o_out = 390.56 - mdot_s*(1443 + 0.172 * 339.5)*(386-T_salt_in)/(mdot_o*…
1000*(1.509 + 0.002496 * 330.56 + 0.0000007888 * 330.56^2));
end
else
UA_OtoS = 14063000;
%This function calls the optimization for the charger
warning off
%options =
optimset('LargeScale','on','Display','iter','TolX',.0000005,'TolFun',.00001,…
'MaxIter',10^6,'MaxFunEval',10^6);
options =
optimset('LargeScale','on','Display','off','TolX',.00000001,'TolFun',.0000005,…
'MaxIter',10^6,'MaxFunEval',10^6);
X=[mdot_o UA_OtoS,T_salt_in];
%call optimiztion routine
80
[mdot_s,Q_diff]=fminsearch(@Storage_Charger,mdot_o*1.6,options,X);
[Q_diff Sol]=Storage_Charger(mdot_s,X);
T_o_out=Sol(1); Q_o=Sol(2); Q_salt_in=Sol(3); mdot_s=Sol(4); eps=Sol(5);
end
function [Q_diff,Sol]=Storage_Charger(mdot_s,X)
% Storage_Charger converges energy balance and eps-NTU
% JK 2009
mdot_o=X(1);
UA_OtoS=X(2);
T4=X(3);
X=[mdot_o UA_OtoS,T4];
T1=393;
T3=386;
dh_salt = 1443 * (T3-T4) + 0.086 * (T3-T4)^2;
%[J/kg]
cps = 1443 + 0.172 * 339.5;
cpo=1000 * (1.509 + 0.002496 * (T1-60) + 0.0000007888 * (T1-60)^2);
%_______________________________________________Oil to Salt
Cmin = min(cpo*mdot_o,cps*mdot_s);
Cmax = max(cpo*mdot_o,cps*mdot_s);
Cr = Cmin/Cmax;
UA_OtoS = UA_OtoS*(mdot_o/396)^0.8;
NTU=UA_OtoS/Cmin;
eps=(1-exp(NTU*(Cr-1)))/(1-Cr*exp(NTU*(Cr-1)));
Q = Cmin*eps*(T1-T4);
T_o_out=T1-((mdot_s*dh_salt*1.03)/(mdot_o*cpo));
Q1=mdot_o*cpo*(T1-T_o_out);
Q_diff=abs(Q-Q1);
Q_salt_in = Q1/1.03;
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Sol=[T_o_out Q Q_salt_in mdot_s eps];
function [T_HotTank,MassStorageH,Q_HotTank,T_HotTank_toHX,dT] =
HotTank(TankAreaH, MassStorageH,Q_HotTank, T_HotTank, mdot_s_in_H,
mdot_s_out_H)
%Hot Tank calculates the temperature, mass, and energy in the hot storage tank
%JK 2009
%Assumptions
%cp stays constant
%Heat loss is f(TankArea) not f(TankArea,T_Tank)
dMstorage_in = mdot_s_in_H;
dMstorage_out = mdot_s_out_H;
T_last = T_HotTank;
T_in =386+273;
%[kg]
%[K]
if Q_HotTank ==0
T_last = T_in;
else
T_last = T_last+273;
end
Q_loss = 68 * TankAreaH;
%[W]
MassStorageH = MassStorageH + dMstorage_in - dMstorage_out;
cp = 1443 + 0.172*(380+273);
%[J/kgK]
Q_in = dMstorage_in*cp*T_in;
%[J]
Q_out = dMstorage_out*cp*T_last;
%Tank_Last
Q_tank = Q_HotTank+Q_in-Q_out;
%[J]
if MassStorageH == 0
T_tank = 0;
dT = 0;
else
T_tank = Q_tank/(MassStorageH*cp);
dT = Q_loss/(MassStorageH*cp);
end
if MassStorageH <=0
if dMstorage_out>0
T_HotTank_toHX =T_last-273;
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T_HotTank = 0;
Q_HotTank = 0;
else
T_HotTank = 0;
Q_HotTank = 0;
T_HotTank_toHX = 0 ;
Percent_loss = 0;
end
else
T_HotTank = T_tank - dT-273;
Q_HotTank = Q_tank - Q_loss;
T_HotTank_toHX = T_last-273;
Percent_loss = Q_loss/Q_tank;
end
function [Pout_LP5 Pout_LP4 Pout_LP3 Pout_LP2 Pin_LP1 Pout_LP1
Pout_HP2 Pin_HP1 Pout_HP1...
%
mdot_LP5,mdot_LP4,mdot_LP3,mdot_LP2,mdot_LP1,mdot_HP2,mdot_HP1] =
TurbinePressure (mdot_w,Tamb)
%mdot_w = 38.8;
%Tamb = 20;
%This function returns the mass flow rates and pressures for the turbine
stages
Pin_HP1_ref = 100;
Pout_HP1_ref = 33.61;
Pin_HP2_ref = 33.61;
Pout_HP2_ref = 18.58;
%Pressure drop from High Pressure out to Low Pressure in
Pin_LP1_ref = 17.10;
Pout_LP1_ref = 7.98;
Pin_LP2_ref = Pout_LP1_ref;
Pout_LP2_ref = 2.73;
Pin_LP3_ref = Pout_LP2_ref;
Pout_LP3_ref = 0.96;
Pin_LP4_ref = Pout_LP3_ref;
Pout_LP4_ref = 0.29;
Pin_LP5_ref = Pout_LP4_ref;
Pout_LP5_ref = 0.08;
mdot_LP5_ref=0.689*38.8;
mdot_LP4_ref=0.709*38.8;
mdot_LP3_ref=0.751*38.8;
mdot_LP2_ref=0.797*38.8;
mdot_LP1_ref=0.849*38.8;
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mdot_HP2_ref=0.925*38.8;
mdot_HP1_ref=38.8;
mdot_LP5=0.689*mdot_w;
mdot_LP4=0.709*mdot_w;
mdot_LP3=0.751*mdot_w;
mdot_LP2=0.797*mdot_w;
mdot_LP1=0.849*mdot_w;
mdot_HP2=0.925*mdot_w;
mdot_HP1=mdot_w;
%Pressure at lowest turbine exit is function of condensing pressure,
%Psat@Tamb
Pout_LP5=XSteam('psat_T',Tamb+7);
Pin_LP5=((mdot_LP5/mdot_LP5_ref)^2*(Pin_LP5_ref^2Pout_LP5_ref^2)+Pout_LP5^2)^0.5;
Pout_LP4=Pin_LP5;
Pin_LP4=((mdot_LP4/mdot_LP4_ref)^2*(Pin_LP4_ref^2Pout_LP4_ref^2)+Pout_LP4^2)^0.5;
Pout_LP3=Pin_LP4;
Pin_LP3=((mdot_LP3/mdot_LP3_ref)^2*(Pin_LP3_ref^2-…
Pout_LP3_ref^2)+Pout_LP3^2)^0.5;
Pout_LP2=Pin_LP3;
Pin_LP2=((mdot_LP2/mdot_LP2_ref)^2*(Pin_LP2_ref^2Pout_LP2_ref^2)+Pout_LP2^2)^0.5;
Pout_LP1=Pin_LP2;
Pin_LP1=((mdot_LP1/mdot_LP1_ref)^2*(Pin_LP1_ref^2Pout_LP1_ref^2)+Pout_LP1^2)^0.5;
%Can make a correction for pressure loss in the reheater stage
Pout_HP2=Pin_LP1;
Pin_HP2=((mdot_HP2/mdot_HP2_ref)^2*(Pin_HP2_ref^2Pout_HP2_ref^2)+Pout_HP2^2)^0.5;
Pout_HP1=Pin_HP2;
Pin_HP1=((mdot_HP1/mdot_HP1_ref)^2*(Pin_HP1_ref^2Pout_HP1_ref^2)+Pout_HP1^2)^0.5;
84
REFERENCES
[1]
http://www.flagsol.com/SEGS_tech.htm
[2]
www.nevadasolarone.net
[3]
Winter, C.J., et al., 1991, “Solar Power Plants,” Springer-Verlag, Berlin,
Heidelber.
[4]
Relloso, Sergio, et al., 2008 “Real Application of Molten Salt Thermal
Storage to Obtain High Capacity Factors in Parabolic Trough Plants,”
42709_1i_5, SolarPACES, Las Vegas, NV.
[5]
Kutscher, Charles F., “Tackling Climate Change in the U.S.”, American
Solar Energy Society, January 2007
[6]
Hermann, Ulf, Kearney D., “Survey of Thermal Energy Storage for
Parabolic Trough Power Plants,” Journal of Solar Energy Engineering,
Vol. 124, pp145-152.
[7]
Price, H., 2003 “A Parabolic Trough Solar Power Plant Simulation Model,”
International Solar Energy Conference, Hawaii Island, Hawaii.
[8]
Lippke, Frank, 1995, “Simulation of the Part-Load Behavior of a 30 MWe
SEGS Plant,” SAND95-1293, Sandia National Laboratories, Albuquerque,
NM.
[9]
Solar Advisor Model (SAM), 2006, National Renewable energy
Laboratory, Golden CO.
[10]
Patnode, Angela, 2006, “Simulation and Performance Evaluation of
Parabolic Trough Solar Power Plants,” Thesis, University of Wisconsin,
Madison.
[11]
Herrmann, Ulf, et al. 2002, “Overview on Thermal Storage Systems,”
Flabeg Solar International GmbH, Workshop on Thermal Storage for
Trough Power Systems.
[12]
Nexant Inc., “USA Trough Initiative Nitrate Salt Heat Transport Fluid:
Rankine Cycle, Steam Generator, and Thermal Storage Analyses.”
January 19, 2001
[13]
Schulte-Fischedick, Jan, et al., 2008, “CFD Analysis of the Cool Down
Behaviour of Molten Salt Thermal Storage Systems,” ASME, Proceedings
of ES2008, Jacksonville, FL.
85
[14]
Kearney, D., et al., 2002, “Evaluation of a Molten Salt Heat Transfer Fluid
in a Parabolic Trough Solar Field,” ASME International Solar Energy
Conference, Reno, NV.
[15]
Incropera, Frank P. and Dewitt, David, “Fundamentals of Heat and Mass
Transfer. 4th Edition. New York: John Wiley and Sons, Inc. 2002.
[16]
Duffie, John, and Beckman William, “Solar Engineering of Thermal
Processes”, John Wiley & Sons Inc., New Jersey, 2006.
[17]
Shah, Ramesh K. and Sekulic, Dusan P., “Fundamentals of Heat
Exchanger Design”, John Wiley & Sons Inc., New Jersey, 2003.
[18]
Nexant Inc., 2001, “Thermal Storage Oil-to-Salt Heat Exchanger Design
and Safety Analysis,” Task Order Authorization Number KAF-9-29765-09,
San Francisco, CA.
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Kopp, Joseph and R.F. Boehm, “Comparison of Two-Tank Indirect
Thermal Storage Designs for Solar Parabolic Trough Power Plants,”
ASME, Proceedings of ES2009, San Francisco, CA.
86
VITA
Graduate College
University of Nevada, Las Vegas
Joseph Kopp
Local Address:
4051 Brighthill Ave
Las Vegas, NV 89121
Degrees:
Bachelor of Arts, Physics, 2004
Lewis & Clark College
Publications:
Joseph Kopp, R.F. Boehm. “Comparison of Two-Tank Indirect Thermal Storage
Designs for Solar Parabolic Trough Power Plants,” Proceedings of ES2009, Energy
Sustainability 2009, July 19-13, San Francisco, CA
R. Cabanillas, J. Kopp. "Measuring Energy Efficiency from a 4kW Dish Concentrator
System Using Older Parabolic Antenna Technology," International Solar Energy
Society-Solar World Congress Proceedings, September 18-21, 2007, Beijing, China
Thesis Title: Two-Tank Indirect Thermal Storage Designs for Solar Parabolic
Trough Power Plants
Thesis Examination Committee:
Chairperson, Robert Boehm, Ph. D.
Committee Member, Yitung Chen, Ph. D
Committee Member. Dan Cook, Ph. D.
Graduate College Representative, Yahia Baghzouz, Ph. D.
87